The present invention relates to methods of controlling the attitude of a satellite placed in an orbit that is low enough for the intensity of the earth""s magnetic field to enable attitude to be measured by means of a three-axis magnetometer and to enable attitude to be changed by causing magneto-couplers carried by the satellite to interact with the earth""s magnetic field.
In practice, this condition is satisfied when at least part of the satellite""s orbit is at an altitude of less than 2000 kilometers (km).
An attitude control method is already known (FR-A-2 742 243 or U.S. Pat. No. 5,788,188) making it possible to reduce the speed of rotation of a satellite, in particular on being released from its launcher, and to orient an axis bound with the satellite so that it is normal to the plane of the orbit. In that method, using a so-called xe2x80x9cB dotxe2x80x9d relationship because it makes use of the derivative of the earth""s magnetic field B, the earth""s magnetic field is measured along three axes of a frame of reference associated with the satellite, the measurements are differentiated with respect to time, the derivatives are multiplied by a gain, and a current representative of the result is passed through magneto-couplers to create magnetic moments tending to keep the satellite stationary relative to the lines of force of the earth""s magnetic field.
Such a method has already been used for controlling the attitude of a satellite carrying flywheels or momentum wheels for creating an internal angular momentum that provides gyroscopic stiffness. However, in some missions, it is desirable to avoid using inertial actuators (flywheels or momentum wheels). By way of example, mention can be made of satellites that are to perform high-precision scientific missions and that have as little on-board mechanism as possible, or satellites for earth observation missions using gyroscopic actuators that are preferably used in normal mode only.
A principle is as follows: a torque is applied to the satellite by means of magneto-couplers to oppose variation in the magnetic field measured along axes bound to the satellite, making use of the fact that the geomagnetic field is locally uniform and any variation in the components of the magnetic field as measured along the axes bound to the satellite constitutes a good approximation to the angular velocities of the satellite. The magneto-couplers are controlled so that they apply torques opposing the measured angular velocities, in order to reduce the speeds of rotation.
Conventionally, the magneto-couplers are controlled for this purpose in such a manner as to create a magnetic moment vector Mc proportional to the derivative with respect to time of the measured terrestrial magnetic field value Bm:
Mc=xe2x88x92k.{dot over (B)}mxe2x80x83xe2x80x83(1) 
In this formula, k designates a gain.
The stabilization caused by this kind of control, which dissipates energy, causes the satellite to turn or spin at a speed 2xcfx890 which is equal to twice its orbital angular frequency about the normal to the orbit.
Spinning at two turns per orbit, even about an axis of greatest angular inertia, possibly does not provide sufficient gyroscopic stiffness to stabilize the satellite.
In addition, it can be preferable to cause the satellite to spin about an axis other than its axis of greatest inertia, for example about the axis normal to the plane of the solar generators that are usually carried by a satellite.
An object of the invention is to provide a method of stabilizing a satellite in low orbit without requiring, at least to any significant extent, of an internal angular momentum, and consequently making it possible to avoid using flywheels or momentum wheels.
To this end, there is provided in particular a method in which the components of the earth""s magnetic field vector are measured along three measurement axes of a frame of reference bound to the satellite (in practice by means of a three-axis magnetometer); the value and the orientation of the earth""s magnetic field as measured in the frame of reference and the derivative {dot over (B)}m of the field vector are deduced therefrom, and magneto-couplers carried by the satellite are controlled to generate a torque for setting the satellite into rotation at an angular frequency xcfx89c about a predetermined spin axis of the satellite, where xcfx89c is greater than 2xcfx890.
The required rotation or spinning rate can be obtained by adding, to the term {dot over (B)}m of formula (1), a reference or set vector {dot over (B)}i representing an angular velocity or bias giving the desired spinning rate. Formula (2) then gives the torque Mc to be applied by means of the magneto-couplers, and thus the current to be applied thereto.
Mc=xe2x88x92k({dot over (B)}mxe2x88x92{dot over (B)}i)xe2x80x83xe2x80x83(2) 
The bias {dot over (B)}i can be calculated, for example from the value of the desired angular velocity vector xcexa9i:
{dot over (B)}i=xcexa9ixc3x97{dot over (B)}m 
which means that the moment, Mc, to be applied is
Mc=kB.({dot over (b)}mxe2x88x92{dot over (b)}i)=kB.({dot over (b)}mxe2x88x92xcexa9ixc3x97{dot over (b)}m)xe2x80x83xe2x80x83(3) 
where {dot over (b)}i is a variation of the set magnetic direction in the frame of reference of the satellite (b designating normalized vector B), and xcexa9i is the desired angular velocity vector for said magnetic direction bi in the satellite frame of reference.
For example, xcexa9i=[0 0 xcfx89i] if it is desired that the magnetic field turns at velocity xcfx89i about the pitch axis Zs (the axis orthogonal to the plane of the solar generators).
Implementing the relationship (2) causes energy to be dissipated and ensures convergence. It tends to cancel out the angular velocity component of the satellite transverse to its spin axis and thus to damp nutation, and in particular the nutation which can exist during injection onto orbit.
A particular spin relationship (2) spinning rate velocity and direction of the spin axis in the satellite frame of reference) will be selected as a function of various parameters, such as the inclination of the orbit relative to the equator and/or the current phase from amongst successive phases of a mission.
The mission can require the spin axis to be oriented other than normally to the plane of the orbit, whereas relationship (2) brings the selected spin axis into this direction.
For example, it can be desirable to orient the spin axis towards the sun so that the solar generators receive maximum power. To do this, the spin axis will be xe2x80x9crightedxe2x80x9d or xe2x80x9cerectedxe2x80x9d so as to bring it onto the direction of the sun, which required (i) measuring the orientation of the satellite relative to the sun and (ii) modifying the relationship (2) for reaching nominal conditions.
The orientation of the sun can be determined using a sun sensor whose aiming direction coincides with the desired spin axis (e.g. normal to the solar generators) and which provides an error signal in two directions.
It is not necessary for the sun sensor to have a characteristic that is linear, since all that matters is the direction of the sun.
During eclipses, the solar sensor does not provide any measurement. Nevertheless the direction of the spin axis remains under control as during a daylight phase in application of relationship (2). The continuity of this relationship ensures that the spin axis becomes progressively realigned with the normal.
Once convergence has been obtained by relationship (2), the sun will be in the sensor""s field of view, which is generally almost hemispherical, except when the difference between the directions of the sun and the plane of the orbit is very small. Under such circumstances, an additional sensor having an aiming direction different from that of the first and possibly having a narrow field of view is provided.
To sum up, implementing control relationship (2) makes it possible to reach a determined initial state of rotation about a spin axis orthogonal to the plane of the orbit and to damp any nutation of whatever origin. Righting or erecting the spin axis can give rise to new nutation; that will be damped by the same process as during initial stabilization using relationship (2).
It can be seen that the method of the invention does not require any thruster, or any gyroscope, and that the only sensors required are a three-axis magnetometer and possibly a wide angle solar sensor so as to be able to see the sun immediately on leaving eclipse, and at the end of stabilization that brings the spin axis to a direction normal to the orbit plane. Only magneto-couplers are used to control attitude. The control relationships are very simple.
The above characteristics and others will appear more clearly on reading the following description of a particular embodiment, given by way of non-limiting example with reference to the accompanying drawings.